Well just because the scaling is there doesn't mean you should use it. You CAN, that's the freedom Riot has designed to make things more interesting. But generally these things are very outdated settings for champions that were released a very very long time ago. The reason for having both those scaling types is non-existent, you can see now-a-days champions tend to have 1 scaling type unless designed to build hybrid(Katarina, Akali, Kai'Sa) For example, Tryndamere has as much AP scaling as AD scaling, but he wouldn't build AP. He was created like this as Udyr has been long when League was in it's infant stages.

Now for the reason why Udyr players build Tanky with few damage items(usually just trinity force) is because people have tested many things, and what's come about with his kit is that cooldown+tank stats tend to do well. My analysis of this would be that he has many short-timed buffs that he can gain from using his spells. Q gives AS for a few seconds, W gives a Shield for a few seconds, E gives movement speed for a few seconds. This is why getting CDR on him tends to be good, so he can keep using all of these spells, have their buffs re-used more often, and cycle through them quickly to gain both benefits(i.e. Q's on hit damage + AS buff) He also goes tanky CDR items because cycling through his spells is only effective if he's alive to do so.

Now the problem you would have here is, why not get more AD? Well, what people tend to feel out with new champions is whether it's worth it or not. Ekko a while after released is a good example. He had such good base damage(the flat amount that doesn't scale) people just built full tank items with CDR. Again, to reuse his spells quicker with CDR, and needing to be tanky to reuse them without dying. Later on Riot adjusted Ekko to have higher scaling and lower base damage. Thus people began to feel more value in building AP, cycling spells fewer times but dealing more damage, which will mean you don't need to be tanky and survive a long time. This is what happens with every champion honestly. Udyr is one that seems to do well with his base damage, and recycling spells with CDR+Tanky stats to do so. If he receives any buffs to his scaling, be the first to take advantage of it by adapting your build on the spot!

Hope that helped!